scholarly journals Passive advection‐dispersion in networks of pipes: Effect of connectivity and relationship to permeability

2016 ◽  
Vol 121 (2) ◽  
pp. 713-728 ◽  
Author(s):  
Y. Bernabé ◽  
Y. Wang ◽  
T. Qi ◽  
M. Li
Keyword(s):  
Passive Advection ◽  
Advection Dispersion

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts 

2021 ◽  
Author(s):  
Alessandro Comolli ◽  
Anne De Wit ◽  
Fabian Brau
Keyword(s):  
Molecular Diffusion ◽  
Early Time ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Calcium Carbonate Precipitation ◽  
Atmospheric Reactions ◽  
Passive Advection ◽  
Reaction Fronts ◽  
Time Regime ◽  
Long Time

<p>The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.</p><p>Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field <em>v<sub>r</sub>(r,z)</em> describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.</p><p>                                  <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&app=m&a=0&c=360a1556c809484116c55812c8c06624&ct=x&pn=gnp.elif&d=1" alt="" width="299" height="299">                                                     <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&app=m&a=0&c=c5a857c3fab835057e3af84001a91d15&ct=x&pn=gnp.elif&d=1" alt="" width="302" height="302"></p><p>                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.</p><p> </p><p>References:</p><p>[1] L. Gálfi, Z. Rácz, Phys. Rev. A 38, 3151 (1988);</p><p>[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);</p><p>[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).</p>

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

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